If you have a fixed monthly data quota on your mobile, it is fair to have some concerns with which applications are eating up most of your megabytes, unbeknownst to you as the user.
Luckily, however, Snapchat uses relatively small data to transmit pictures back and forth. Roughly between 30 to 50 KB. This means that transmission can occur very swiftly and hardly at the expense of your data allowance.
If you still have concerns, or you have run out of your monthly data, the best idea is to find ways to connect to wifi as often as possible.
When you are connected to wifi, you can roam the internet and download as much as you wish without this affecting your data. In general, however, snapchat does not use a lot of data, if you are using it a moderate amount.
I hope this helps.